The context of the work presented in this thesis is the digital geometry. This research area is devoted to the automatic analysis of objects in digital images. Indeed, many acquisition systems provide regular data in dimension 2 and 3. In order to design efficient analysis algorithms, Euclidean geometry theorems and algorithms should be redesign to consider specificities of the digital space. In this framework, we have first investigated fundamental objects (grids, straight lines, circles,...), allowing us to define efficient geometrical reconstruction algorithms. Then, we have considered high performance algorithms to perform volumetric analysis of digital objects (distance transformation, medial axis,...).